Method of high-resolution distance processing

ABSTRACT

The method carries out a measurement of the distance from the ground of an aircraft by undertaking the emission of waveforms making it possible to obtain, after demodulation, of the signals received in return and sampling of the demodulated signals at a frequency F éch , two signals E* 0 (t) and E* 1 (t), taking the form of two frequency ramps, of respective slopes K 0  and K 1 , of respective passbands B 0  and B 1  and of respective durations T E0  and T E1 , the N-point FFT spectral analysis of which is carried out. The values of the durations T E0  and T E1  as well as those of the passbands B 0  and B 1 , are defined in such a way as to be able to determine, on the basis of the spectra of the signals E* 0 (t) and E* 1 (t), a measurement of non-ambiguous distance d 1  covering the maximum distance d max  to be instrumented and an ambiguous distance d 0  exhibiting the desired distance resolution. The distance d to be measured being determined by combining these two measurements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to foreign French patent applicationNo. FR 1800838, filed on Aug. 2, 2018, the disclosure of which isincorporated by reference in its entirety.

FIELD OF THE INVENTION

The invention pertains to the general field of airborne systems,helicopters or aircraft with (aeroplanes) or without (drones) a pilotfor example.

It pertains more particularly to the distance and speed measurementscarried out by a radar embedded on board one or the other of thesecraft.

BACKGROUND

To carry out a measurement of distance by means of an airborne radar itis known to adopt a mode of operation implementing a waveformconstituted by a recurrent emission, of emission duration T_(E),linearly modulated in frequency over time. Indeed, such a waveform makesit possible in a known manner to determine, in a simple manner, thedelay τ between the signal emitted e(t) and the signal received r(t), byconsidering the corresponding time-frequency representations.

The basic principle of such a mode of operation is illustrated byFIG. 1. This principle consists in emitting a signal e₀(t) whosefrequency exhibits a positive linear variation during the first half ofa time interval TE and a signal e₁(t) whose frequency exhibits anegative linear variation during the second half of the same timeinterval; the frequency of the signal emitted varying in a band B.

The radioelectric signal emitted e₀(t), radiated by an antenna in thedirection of the ground, is here linearly modulated in frequency as afunction of time, so that it is expressed by:e ₀(t)=e ^(i2πKt) ²   [1]

with

${K = \frac{B}{T_{E}}},$B representing the frequency band emitted and T_(E) the emission time,or illumination time.

Likewise, the signal r₀(t), reflected by the ground subsequent to thisemission and received by the radar, is a signal likewise linearlymodulated in frequency, whose frequency varies over a band B, whichexhibits, with respect to the signal emitted e₀(t), a time shift, adelay, τ, and a shift in frequency f_(D) due to the Doppler effectengendered by the motion of the carrier, which are functions of thedistance d separating the radar from the ground.

Hence, the general expression for the reflected signal received by theradar is:r ₀(t)=e ^(i·2·Π(Kt(t−τ)+f) ^(D) ^(t)) =e ₀(t)·e ^(i·2·Π(−Kτ+f) ^(D)^()t)  [2]

So that the transpositions obtained after mixing of r₀(t) and e₀(t) areexpressed by:

r₀(t)·e₀(t) which will be eliminated after filtering

and

$\begin{matrix}{\frac{r_{0}(t)}{e_{0}(t)} = e^{i{{.2}.{\Pi({{{- K}\;\tau} + f_{D}})}}t}} & \lbrack 3\rbrack\end{matrix}$

In a known manner, the delay τ of r(t) with respect to e(t) is equal to

$\tau = \frac{2.d}{c}$where c represents the speed of light in vacuo.

The signals e₁(t) and r1(t) exhibit for their part, respectively,expressions similar to e₀(t) and r₀(t) by means of a temporaltranslation equal to T_(E)/2.

In a representation in the time/frequency plane the signal e(t) can bedefined, for instants lying between 0 and T_(E)/2, by the followingnormalized equation:E ₀(t)=Kt  [4]

E₀(t) represents the value of the frequency of the signal e(t) at theinstant t considered. It takes the form of a frequency ramp with acoefficient K.

In an analogous manner, the signal r(t) can be defined, for instantslying between 0 and T_(E)/2, by the following normalized equation:R _(0(t)) =K(t−τ)+f _(D)  [5]

R₀(t) represents the value of the frequency of the signal r₀(t) at theinstant t considered. It takes the form of a frequency ramp similar toE₀(t) but shifted by a time interval τ on the x-axis (abscissa axis) andby a frequency f_(D) on the y-axis (frequency axis); τ representing thedelay related to the distance d between the radar and the ground andf_(D) the Doppler frequency.

In this time/frequency representation, the difference between the signalreceived R₀(t) and the signal emitted E₀(t) therefore appears as aconstant frequency magnitude equal to:ΔF ₀ =−K·τ+f _(D)  [6]

In an analogous manner, the signals e₁(t) and r₁(t) can be defined, forinstants lying between T_(E)/2 and T_(E), by the following normalizedequations:E ₁(t)=−Kt+B  [7]andR _(1(t)) =−K·(t−τ)+B+f _(D)  [8]

E₁(t) therefore takes the form of a frequency ramp falling from a valueB with a coefficient K and R₁(t) in the form of a frequency ramp similarto E₁(t) but shifted by a time interval τ on the x-axis (abscissa axis)and by a frequency f_(D) on the y-axis (frequency axis).

The difference between the signal received R1(t) and the signal emittedE1(t) therefore appears as a constant frequency magnitude equal to:ΔF ₁ =K·τ+f _(D)  [9]

Hence, by considering relations [6] and [9], we may write:S=ΔF ₁ +ΔF ₀=2f _(D)  [10]E=ΔF ₁ −ΔF ₀=2K·τ  [11]

Thus, if these magnitudes E and S are considered, it is noted that theirmeasurements advantageously make it possible to determine respectivelythe Doppler frequency F_(D) and the delay τ.

However, in the context of the present invention, one is concerned onlywith the determination of the distance, through τ, so that only relation[13] is exploited.

It should be noted here that the magnitudes E_(i)(t), R_(i)(t), ΔF_(i),S and E are dimensionally equivalent to frequencies and that E,difference of frequencies, is always positive since it is proportionalto distance.

The expression for e(t) in the amplitude/time domain is given by thefollowing relation:e(t)=Ae ^(−i4πKτt)  [12]where 4πKτ represents 2π times the frequency of variation of E

In practice the signals ΔF₁ and ΔF₀ are sampled with a frequencyF_(éch). The signal e*=e(n·T_(éch)), obtained by subtraction of thesamples of ΔF₁(n·T_(eéch)) and ΔF₀(n·T_(éch)), consists of a sequence ofsamples e*, and can form the subject of a spectral decomposition, forexample by FFT, the spectrum formed consisting of frequency samplesdenoted E_((F))*.

Hence, the determination of the spectrum of the signal e* makes itpossible to determine the frequency, Kτ, of the signal e* and hence thedelay τ and therefore the distance d that one wishes to measure.

It is recalled, however, as illustrated by FIG. 2, that the spectrum ofthe signal e*, signal e(t) sampled at the frequency F_(éch), takes theform of an elementary spectrum of width equal to F_(éch), replicated inthe frequency space with a periodicity equal to F_(éch).

Hence, the spectral decomposition of e* makes it possible to determine,in a non-ambiguous manner, the spectrum of frequencies (the centralfrequency) of the signal E_((F))* provided that the frequency bandoccupied by E_((F))* is less than F_(éch)/2.

If the frequency band occupied by E_((F))* is greater than this value,then, in a known manner, an aliasing of the spectrum of E_((F))* in aband [−F_(éch)/2, F_(éch)/2] replicated periodically around frequencieswhich are multiples of the frequency F_(éch) is seen. In the latter casethe frequency of the signal e* (and therefore the delay τ) can only bedetermined modulo F_(éch).

To circumvent ambiguity problems generated by the sampling of the signale*, a known solution consists in increasing the sampling frequencyF_(éch) so as to ensure that, for the spectral resolution considered,the ambiguous frequency is situated beyond the maximum frequency of thesignal e*.

However, such a way of proceeding makes it necessary to increase thenumber of coefficients of the FFT that is used for the spectraldecomposition, and therefore to process a more sizable number of signalsamples, failing which a degradation in the frequency resolution (andtherefore in the distance resolution) of the spectral response obtainedis seen. However, such a rise in the calculational load makes itnecessary to have sufficient calculational capabilities to carry out, inthe time available, an FFT calculation on a number of sufficient points.

Hence, according to the value of the frequency f of the signal e*, it issometimes difficult, without having the necessary calculationalcapabilities, to carry out a measurement of distance over a givendistance span with a satisfactory resolution, on the basis of the simpleFFT spectral decomposition of the signal e* described above.

In such a context, one is constrained to use an alternativedetermination scheme, or to implement complementary processing steps.

The European patent application filed by the applicant and publishedunder the reference EP2605037A1 proposes an alternative measurementscheme to that described above, which implements three separateemission/reception pathways; the signal processed by each pathway,constructed by repeating a signal of duration T_(E) consisting of apositive frequency ramp of duration T_(E)/2 followed by a negative rampof duration T_(E)/2, being sampled and decomposed spectrally.

SUMMARY OF THE INVENTION

An aim of the invention is to propose a solution, based on the emissionof frequency ramps, making it possible to take advantage of the use of asimple mode of operation to measure the radar-ground distance by simpleFFT spectral analysis of the sampled signal e* described above,resulting from the mixing of the signal received r(t) and of the signalemitted e(t), while making it possible to circumvent the drawbackscaused by possible distance ambiguities resulting from the sampling atF_(éch).

The appearance of ambiguities is caused by the compromise that has to bemade between the use of a sampling frequency sufficient to avoid anyspectral ambiguity, the number of measurements on which the FFT must beperformed to obtain the desired spectral resolution and thecalculational capability available to perform an FFT on the desirednumber of points.

To this effect the subject of the invention is a method for determiningin real time the distance, d, from the ground of an aircraft by radarmeasurements, the said distance d being determined, for a span ofdistances extending up to a given distance d_(max), with a givenconstant resolution R_(d0).

The method according to the invention implements the followingoperations:

the emission of at least two successive frequency ramps and thereception of the signals reflected by the ground subsequent to theseemissions;

the construction, on the basis of the reflected signals received, of twosignals E₀(t) and E₁(t) each corresponding to the reflected signal r₀(t)or r₁(t) originating from the successive emissions of two waveformse₀(t) and e₁(t), after demodulation of the signals r₀(t) and r₁(t) bythe corresponding wave e₀(t) or e₁(t) and sampling of the demodulatedsignal at a given frequency F_(éch);

the said waveforms e₀(t) and e₁(t) being represented in a“time-frequency” space by two frequency ramps exhibiting respectiveslopes of variation K₀ and K₁, on two frequency bands B₀ and B₁ whoseratio B₁/B₀ is a given integer number, the band B₀ being determined as afunction of the distance resolution R_(d0) by the relation:B ₀ =c/2R _(d0),the slope K₁ being determined as a function of the distance d_(max) bythe relation:

${K_{1} = {\frac{c}{2} \cdot \frac{F_{\overset{'}{e}{ch}}}{2\;{\alpha \cdot d_{1\;\max}}}}};$the slopes K₀ and K₁ being respectively given by the relationsK ₀ =B ₀ /T _(E0) and K ₁ =B ₁ /T _(E1)where T_(E0) and T_(E1) represent the respective durations of emissionof the waveforms e₀(t) and e₁(t),

the application of an FFT, on N samples, to the signals E₀(t) and E₁(t)and the determination of the spectral components E₀ and E₁ correspondingto the said signals, E₀ corresponding to the component of lowestfrequency of the spectrum of E₀(t);

the determination, on the basis of the spectral components E₀ and E₁, ofthe distances measured d₀ and d₁ by means of the waveforms e₀(t) ande₁(t) corresponding respectively to the spectral components E₀ and E₁,d₀ and d₁ being given by the relations:

$d_{0} = {{{\frac{c}{2} \cdot \frac{E_{0}}{\alpha\; K_{0}}}\mspace{14mu}{and}{\mspace{11mu}\;}d_{1}} = {\frac{c}{2} \cdot \frac{E_{1}}{\alpha\; K_{1}}}}$

the determination, on the basis of d₀ and d₁, of the distance d to bemeasured, d being given by the relation:d=M·d _(0max) +d ₀

with

$d_{0\;\max} = {{\frac{c}{2} \cdot \frac{F_{0\;\max}}{\alpha\; K_{0}}} = {\frac{c}{2} \cdot \frac{F_{\overset{'}{e}{ch}}}{2\;\alpha\; K_{0}}}}$and$M = {{{INT}\left( \frac{d_{1}}{d_{0\;\max}} \right)} = {{{INT}\left( {2 \cdot E_{1} \cdot T_{\overset{'}{e}{ch}}} \right)}.}}$

According to a preferred mode of implementation, the method according tothe invention mainly comprises the following steps:

a first step during which are determined the slopes K₀ and K₁, andfrequency bands B₀ and B₁ characterizing the two signals e₀(t) and e₁(t)as well as the durations of emission T_(E0) and T_(E1) of these twosignals; this first step being carried out while taking into account thefollowing parameters:

-   -   maximum distance measured: d_(max),    -   distance resolution required: R_(d0),    -   frequency of sampling of the signals received by the radar:        F_(éch),    -   number N of points on which the spectral decomposition of the        signals must be performed;

a second emission step during which:

-   -   the radar emits at least two waves corresponding to a chosen        type of emission, at least one of these waves consisting of a        frequency ramp of band B₀ and of slope K₀;    -   the radar receives the reflected signals resulting from the        reflection by the ground of the emitted waves;    -   the signals E₀(t) and E₁(t) are formed on the basis of the        reflected signals received;

a third step during which is carried out the spectral decomposition byFFT on N points of the signals E₀(t) and E₁(t) and the determination ofthe spectral components E₀ and E₁;

a fourth step during which is carried out the calculation of thedistance d on the basis of E₀ and E₁.

Moreover, according to various provisions that can each be consideredseparately or that can be considered in combination, the methodaccording to the invention can moreover exhibit the technicalcharacteristics hereinafter.

Thus, according to a particular provision, the fourth step comprises:

a first sub-step of calculating the distance d₁ defined by:

$d_{1} = {\frac{c}{2} \cdot \frac{G_{1}}{\alpha\; K_{1}}}$where G₁ represents the integer part of the spectrum of E1(t)

a second sub-step of calculating the scale factor M defined by:

${M = {{INT}\left( \frac{2\; E_{1}}{F_{\overset{'}{e}{ch}}} \right)}};$

a third sub-step of calculating the distance d₀ defined by:

$d_{0} = {\frac{c}{2} \cdot \frac{H_{0}}{\alpha\; K_{0}}}$where H₀ represents the integer part of the value of the first spectralline, E₀, of the spectrum of E0(t);

a fourth sub-step of calculating the distance d, defined by:d=M·d _(0max) +d ₀.

According to another particular provision, the waveforms emitted by theradar in the course of the second step of the method consist of a firstfrequency ramp e₀(t) of band B₀ and of slope K₀ followed by a secondfrequency ramp e₁(t) of band B₁ and of slope K₁.

According to a particular provision, the signal e₀(t) and the signale₁(t) have distinct durations of respective emission T_(E0) and T_(E1)and occupy one and the same frequency band B, so that their respectiveslopes K₀ and K₁ are expressed by:

$K_{0} = {{\frac{B}{T_{E\; 0}}\mspace{14mu}{and}{\mspace{11mu}\;}K_{1}} = {\frac{B}{T_{E\; 1}}.}}$

According to another particular provision, the signals E₀(t) and E₁(t)are obtained after demodulation of the signals received r₀(t) and r₁(t)by the signals emitted e₀(t) and e₁(t), the signals E₀(t) and E₁(t)being thereafter sampled in the course of the third step at thefrequency F_(éch) so as to obtain the signals E*₀(t) and E*₁(t), the FFTspectral analysis of which is carried out.

According to another particular provision, the waveforms emitted by theradar in the course of the second step of the method consist of arecurrent string of N identical frequency ramps e₀(t−nT_(E0)), mutuallyshifted in time by a duration T_(E0) equal to the emission time of aramp, of band B and of duration T_(E0).

According to another particular provision, for each of the N frequencyramps emitted, the signal the signal E₀(t) obtained by demodulation ofthe signal received by the signal emitted is sampled to obtain thecorresponding signal E*₀(t), and then a signal E*₁(t) is constructed byconsidering a sample of the signal E*₀(t) formed for each of the N rampsemitted, the signal E*₁(t) consisting of the N samples thus tapped off.

According to another particular provision, for the nth frequency rampe₀(t) emitted the signal received r₀(t) is demodulated by applying aphase shift equal to

$n \cdot \frac{2.\pi}{N}$to the local oscillator of the radar receiver.

According to another particular provision, for each of the N signalsE*₀(t) formed, one taps off the sample corresponding the instant t_(n)determined by the expression:

${t_{n} = {{n \cdot T_{E\; 0}} + {n \cdot \frac{T_{E\; 0}}{N}}}},$in which n represents the rank, in the ramp string of frequency rampsemitted, of the frequency ramp n corresponding to the signal E*₀(t)considered.

From a functional point of view, the method thus carries out ameasurement of the distance d from the ground of an aircraft, with agiven distance resolution R_(d0) and for a measurement span extending upto a given distance dmax, by proceeding in the manner of a vernierexhibiting a main measurement scale allowing a measurement d₁ ofdistance over the desired span of values (from 0 to d_(max)) with agiven resolution R_(d1) and a complementary measurement scale making itpossible to correct the previous distance measurement by means of ameasurement d₀, valid over a span of distances d_(0max) which is smallerthan d_(max), obtained with the desired resolution.

BRIEF DESCRIPTION OF THE DRAWINGS

The characteristics and advantages of the invention will be betterappreciated by virtue of the description which follows, whichdescription is supported by the appended figures which present:

FIG. 1, a simultaneous representation in a time-frequency frame of anemission signal in rising and falling double frequency ramp form and ofthe signal received by the radar after reflection on the ground;

FIG. 2, a frequency representation illustrating the phenomenon offrequency ambiguity that may be caused by the sampling at a frequencyF_(éch) of the signal e(t) resulting from a waveform such as thatillustrated by FIG. 1;

FIG. 3, a basic flowchart of the various steps of the method accordingto the invention;

FIG. 4, a basic flowchart of the various sub-steps of the fourth step ofthe method according to the invention;

FIG. 5, an illustration of the operating principle of the methodaccording to the invention;

FIGS. 6a and 6b , the representations in a time-frequency frame of twovariants of a first exemplary waveform allowing the implementation ofthe method according to the invention and of the waveforms received bythe radar after reflection on the ground;

FIGS. 7 and 8, representations in a time-frequency frame of a secondexemplary waveform allowing the implementation of the method accordingto the invention according to a second form of implementation.

It should be noted that, in the appended figures, one and the samefunctional or structural element bears, preferably, one and the samereference symbol.

DETAILED DESCRIPTION

As stated above, the method according to the invention implements theprinciple consisting in emitting a type of simple waveform consisting ofsuccessive frequency ramps and in determining the distance d whichseparates the aircraft from the ground by calculating the frequency gapand the delay existing between the signal e(t) (a frequency ramp)emitted by the radar and the signal r(t) reflected by the ground andreceived by this same radar.

Accordingly, the method according to the invention implements aprocessing comprising the operations described hereinafter, byconsidering the signal E(t) obtained as indicated above:

${{E(t)} = {\frac{r(t)}{e(t)} = e^{i{{.2}.{\Pi({{{- K}\;\tau} + f_{D}})}^{t}}}}},$whose representation in a time-frequency space is defined by thefollowing relationΔF=−K·τ+F _(D)

According to the invention, the signal ΔF is sampled at the frequencyF_(éch) so that the signal e*=e(n·T_(éch)) obtained after samplingconsists of M samples.

The signal e* thereafter forms the subject of a spectral decomposition,by FFT on N points in a preferential manner, the spectrum E*(F) thusformed consisting of N frequency samples.

It should be noted that the signal thus formed is considered to beessentially dependent on the delay τ, the frequency f_(D) beingconsidered to be generally negligible despite choosing in this regardthe slope of variation K of the frequency ramp emitted.

The operations described above are executed by successively consideringtwo values of slope of variation K₀ and K₁ in such a way that twospectra E*₀(F) and E*₁(F) are obtained after execution. These twospectra are thereafter utilized jointly.

According to the invention, the slopes K₀ and K₁ of the signalsconsidered are determined by taking into account the measurementrequirements consisting of the maximum distance value d_(max), as wellas the distance resolution R_(d0) desired for the distance measurementperformed. The slope K₀ is determined in such a way as to obtain asignal E₀(t) whose passband makes it possible to obtain the desireddistance resolution, while the slope K₁ is determined in such a way asto measure distance values d extending up to a value d_(max). Hence theslope K₁ is of value lower than the slope K₀.

These two slopes are moreover determined by various functionalparameters, related to the hardware operation of the device whichcarries out the calculation of the distance d:

the period T_(éch) of the signals sampling clock which determines, in aknown manner, the maximum frequency of the spectrum of the signalsamplable without aliasing: F_(max)=½·T_(éch);

the number of points N on which the FFT spectral decomposition iscalculated. This number of points determines the frequency resolutionr_(f0) of the spectrum of the signal E₀(t) or E₁(t) considered.

As illustrated by the schematic of FIG. 3, the method according to theinvention mainly comprises four steps.

In the course of a first step 31, the method according to the inventionutilizes the parameters cited above to determine the values of theslopes K₀ and K₁ and the bands B₀ and B₁ corresponding to the frequencyvariations of the signals E₀(t) and E₁(t) exhibiting the desiredcharacteristics.

Accordingly, it executes in particular the following operations:

1) Calculation of the band B₀ of the signal E₀(t).

In a known manner, B₀ is determined as a function of the distanceresolution desired by the relation:

$\begin{matrix}{B_{0} = \frac{c}{2 \cdot R_{D\; 0}}} & \lbrack 13\rbrack\end{matrix}$

2) Calculation of the duration T_(E0) of the signal E₀(t). T_(E0) isgiven by:T _(E0) =N·T _(éch)  [14]

3) Calculation of the slope K₀:

$\begin{matrix}{K_{0} = \frac{B_{0}}{T_{E\; 0}}} & \lbrack 15\rbrack\end{matrix}$

4) Calculation of the maximum distance measurable without ambiguityd_(0max) and of the corresponding delay τ_(0max).

τ_(0max) and d_(0max) are given respectively by the following relations:

$\begin{matrix}{\tau_{0\max} = {{\frac{F_{\max}}{2K_{0}}\mspace{14mu}{with}\mspace{14mu} F_{\max}} = \frac{1}{2 \cdot T_{\overset{'}{e}{ch}}}}} & \lbrack 16\rbrack \\{and} & \; \\{d_{0\max} = \frac{c \cdot F_{\overset{'}{e}{ch}}}{4K_{0}}} & \lbrack 17\rbrack\end{matrix}$

5) Calculation of the slope K₁.

The slope K₁ is determined by taking account of the maximum distance tobe measured d_(max) and the maximum frequency of the signal E(t), havingregard to the sampling frequency F_(éch). It is expressed by:

$\begin{matrix}{K_{1} = {\frac{F_{\overset{'}{e}{ch}}}{4 \cdot \tau_{\max}} = \frac{c \cdot F_{\overset{'}{e}{ch}}}{8 \cdot d_{\max}}}} & \lbrack 18\rbrack\end{matrix}$

It should be noted that, K₁ being determined, the shape of the signalE₁(t) is preferentially determined by altering the band B₁.

Next, in the course of a second step 32 of the method according to theinvention, the radar undertakes the emission of waveforms making itpossible to obtain the signals E₀(t) and E₁(t) and undertakes thereception of the corresponding reflected signals to form these signalsE₀(t) and E₁(t).

As is described further on in the present description, the waveformsemitted may be of various types chosen elsewhere. However, they have thecommon characteristic of making it possible on the basis of thereflected signals received by the radar to form the signals E₀(t) andE₁(t). The type of waveform to be implemented constitutes in this regardan operating parameter taken into account in the course of this secondstep.

The values of K₀, K₁, B₀ and B₁ being thus determined in step 31, it isadvantageously possible to determine, according to the envisaged type offrequency ramps, the characteristics of the frequency ramps to beemitted so as to obtain the signals E₀(t) and E₁(t).

The third step 33 of the method according to the invention implementsthe frequency processing of the signals E₀(t) and E₁(t) in such a way asto determine the components of the spectra of the signals E₀(t) andE₁(t) sampled at the frequency F_(éch).

It should be noted here that, on account of the values of thoseoperating parameters taken into account by the method according to theinvention, for a given instrumented maximum distance d_(max), thespectrum of E₁(t) consists of a single line E₁, while the spectrum ofE₀(t) consists of a comb of lines of period F_(éch), of which the lineF₀ of lowest frequency lies between 0 and

$\frac{F_{\overset{'}{e}{ch}}}{2}.$

The fourth step 34 of the method according to the invention consists,for its part, of the determination on the basis of the spectra of thesampled signals E₀(t) and E₁(t), in determining a measurement of thedistance d.

Accordingly, as illustrated by FIG. 4, step 34 of the method accordingto the invention implements various sub-steps itself.

Step 34 thus comprises a first sub-step 341 during which the signalE₁(t) is used to calculate the distance d₁ which corresponds to thedistance d measured on the basis of the signal E₁(t). The distance d₁ isgiven by the following relation:

$\begin{matrix}{d_{1} = {\frac{c}{2} \cdot \frac{G_{1}}{\alpha\; K_{1}}}} & \lbrack 19\rbrack\end{matrix}$G₁ represents the integer part of the spectrum of E1(t), defined as afunction of the delay τ by the relation:E ₁ =α·K ₁·τ  [20]

The distance resolution of E₁ being equal to

${r_{d\; 1} = \frac{c}{2B_{1}}},G_{1}$represents here the value of the frequency component of E₁, which may bewritten as a function of the frequency resolution r_(F0):

$\begin{matrix}{G_{1} = {{{INT}\left( \frac{E_{1}}{r_{F\; 0}} \right)} \cdot r_{F\; 0}}} & \lbrack 21\rbrack\end{matrix}$

It should be noted that the distance d₁ advantageously gives ameasurement of the distance d which is valid over the whole distancespan extending up to the value d_(max). However, this distancemeasurement is obtained with a resolution r_(d1) lower than the distanceresolution r_(d0) sought.

Step 34 also comprises a second sub-step 342, during which the methodaccording to the invention calculates the factor M defined by therelation:

$\begin{matrix}{M = {{{INT}\left( \frac{E_{1}}{F_{\max}} \right)} = {{{INT}\left( \frac{2E_{1}}{F_{\overset{'}{e}{ch}}} \right)} = {{{INT}\left( {2 \cdot E_{1} \cdot T_{\overset{'}{e}{ch}}} \right)} = {{INT}\left( {\frac{d_{1}}{d_{0\max}} \cdot \frac{K_{0}}{K_{1}}} \right)}}}}} & \lbrack 22\rbrack\end{matrix}$where INT represents the “integer part” function

Step 34 further comprises a third sub-step 343, during which the methodaccording to the invention determines, on the basis of the signal E₀(t),the distance d₀ given by the following relation:

$\begin{matrix}{{d_{0} = {\frac{c}{2} \cdot \frac{H_{0}}{\alpha\; K_{0}}}};} & \lbrack 23\rbrack\end{matrix}$H₀ represents the integer part of the value of the first spectral line,E₀, of the spectrum of E0(t) defined as a function of the delay τ by therelation:E ₀ =α·K ₀·τ  [24]so that we may write:

$\begin{matrix}{H_{0} = {{{INT}\left( \frac{E_{0}}{r_{F\; 0}} \right)} \cdot r_{F\; 0}}} & \lbrack 25\rbrack\end{matrix}$

Step 34 finally comprises a fourth sub-step 344, during which the methodaccording to the invention calculates the value of the distance dmeasured, d being given by the relation:d=M·d _(0max) +d ₀  [26]

As was mentioned above, the waveforms emitted during step 32 can be ofvarious types chosen elsewhere. However, they have the commoncharacteristic of making it possible to form signals E₀(t) and E₁(t)defined by their respective bands B₀ and B₁ and their respective slopesof frequency variation K₀ and K₁. The type of waveform to be implementedconstitutes in this regard an operating parameter taken into account inthe course of this second step.

It should be noted that the main functional parameters, which determinethe bands B₀ and B₁ as well as the slopes K₀ and K₁ are:

functional parameters:

-   -   the distance resolution: R_(d0);    -   the maximum distance to be measured: d_(1 max);

parameters related to the hardware structure intended to implement themethod according to the invention:

the signals sampling period, T_(éch), which fixes the maximum frequencyof the sampled signals:

${F_{\max} = \frac{1}{2 \cdot T_{\overset{'}{e}{ch}}}};$

the number N of points on which the FFT is applied to the signals E₀(t)and E₁(t). This number N determines the frequency resolution R_(f0) ofthe spectrum formed after FFT.

The illustration of FIG. 5 makes it possible to represent from a formalpoint of view the operating principle of the method according to theinvention, which can be considered to be an analysis of the spectrum ofthe signal E₁(t) described above by considering two distinct,superposed, frequency references (i.e. two distance references) 51 and52 which are multiples of one another, these two references beingrelated to the respective values of the respective passbands B₀ and B₁and slopes K₀ and K₁ of the emitted waveforms.

The reference 51 with the larger spacing, a spacing

${P_{1}\left( {P_{1} = {R_{d\; 1} = {\frac{c}{2 \cdot B_{1}} = {\frac{c}{2 \cdot K_{1}}T_{E}}}}} \right)},$makes it possible to measure, with a frequency resolution correspondingto the distance resolution R_(d1), which is however insufficient, thefrequency E of the spectrum of the sampled signal E(t)* which actuallycorresponds to the frequency of the real signal E(t) and therefore tothe true distance d; the measured frequency E lying in a given intervalof frequencies of width equal to the spacing P1.

The scale 52 with the smaller spacing, a spacing P2, makes it possibleto locate the frequency E in a restricted frequency interval,corresponding to the distance resolution R_(d0) desired, inside thefrequency interval of width P1 including the frequency E.

In the illustration of FIG. 5 the distance scales corresponding to thefrequency scales have been depicted directly.

Hereinafter in the document, two examples of waveforms that may be usedfor the implementation of the method according to the invention areproposed by way of example.

It should be noted that the choice of the waveforms to be emitted, whichchoice is made taking account of the functional parameters mentionedabove, affects only the execution of the second step 32 of the methodaccording to the invention. Accordingly, the elements of the descriptionwhich relate to the exemplary implementations of the method according tothe invention pertain mainly to the second step 32 of the methodaccording to the invention.

According to the first form of implementation presented here,illustrated by FIG. 6a , the emitted waveforms consist of two distinctfrequency ramps 61 and 62, exhibiting slopes of variation respectivelyequal to K₀ and K₁, the slope K₀ being greater than the slope K₁. Thefirst ramp 31 is a ramp of durations T_(E0), whose passband takes avalue B₀ while the second ramp 62 is a ramp of durations T_(E1), equalto T_(E0), whose passband takes a value B₁. We can therefore write:

$K_{0} = {{\frac{B_{0}}{T_{E\; 0}}\mspace{14mu}{and}\mspace{14mu} K_{1}} = \frac{B_{1}}{T_{E\; 0}}}$

In this first exemplary implementation the two frequency ramps 61 and 62are emitted successively by the radar in the course of step 62, so thatthe signals E₀(t) and E₁(t) are respectively formed directly by carryingout the demodulation by the frequency ramp 61 of the reflected signal 63received by the radar after emission of this first frequency ramp andthe demodulation by the frequency ramp 62 of the reflected signal 64received by the radar after emission of this second frequency ramp, andthen by filtering the signal produced so as to preserve only the signal

${E(t)} = {\frac{r(t)}{e(t)} = {e^{{i \cdot 2 \cdot {\pi{({{{- K}\;\tau} + f_{D}})}}}t}.}}$

We thus obtain the signals:

$\begin{matrix}{{E_{0}(t)} = {\frac{r_{0}(t)}{e_{0}(t)} = e^{{i \cdot 2 \cdot {\pi{({{{- K_{0}}\tau} + f_{D}})}}}t}}} & \lbrack 27\rbrack \\{and} & \; \\{{E_{1}(t)} = {\frac{r_{1}(t)}{e_{1}(t)} = e^{{i \cdot 2 \cdot {\pi{({{{- K_{1}}\tau} + f_{D}})}}}t}}} & \lbrack 28\rbrack\end{matrix}$

The signals E₀(t) and E₁(t) being thus obtained on the basis of the tworamps 61 and 62, the method according to the invention proceeds in themanner described above.

In the form of implementation described above, it is considered that thetwo frequency ramps 61 and 62 emitted have one and the same durationT_(E0), so that the slopes K₀ and K₁ are obtained by altering therespective passbands B₀ and B₁ of the two ramps. Signals are thusprocessed that exhibit two distinct distance resolutions R_(d0) andR_(d1) of which R_(d0) represents the distance resolution sought for thecalculation of the distance d.

However it should be noted that, in another form of implementation ofthe method according to the invention, illustrated by FIG. 6b , it ispossible to consider two frequency ramps 61 and 62 emitted with distinctdurations T_(E0) and T_(E1), on one and the same band B(B₀=B₁=B), sothat the slopes K₀ et K₁ are determined by altering the respectivevalues of T_(E0) and T_(E1).

In this case, the processing is carried out by applying an FFT on N₀points to the signal E*₀(t) and on N₁ points to the signal E*₁(t)thereby making it possible to adjust T_(E0)=N₀·T_(éch) andT_(E1)=N₁·T_(éch) in such a way that T_(E1) is a multiple of T_(E0).Signals are thus processed by considering two distinct frequencyresolutions

$R_{f\; 0} = {{\frac{1}{T_{E\; 0}}\mspace{14mu}{and}\mspace{14mu} R_{f\; 1}} = {\frac{1}{T_{E\; 1}}.}}$

It should be noted here that the spacing P1 is then defined by thefrequency resolution R_(f1) since the distance resolution is constantbecause there is emission of an identical frequency band

${B\left( {r_{D} = \frac{c}{2 \cdot B}} \right)}.$

This form of implementation, similar in its principle to the formdescribed above, allows the value of the distance to be obtained morerapidly in the least fine resolution.

It is also possible, in a generalized manner, in a form ofimplementation analogous to the previous form, to envisage undertakingthe emission of two frequency ramps 61 and 62 exhibiting distinctdurations T_(E0) and T_(E1) and also distinct bands B₀ and B₁. It isthus possible to adjust the values of the slopes K₀ and K₁ by alteringeither the respective values of T_(E0) and T_(E1) and/or the respectivevalues of B₀ and B₁.

FIGS. 7 and 8 illustrate the operating principle of a second form ofimplementation of the method according to the invention.

This form of implementation consists in emitting in a recurrent manner,with a period T₀, a series of N identical elementary frequency ramps 71of slope K₀ and of duration T_(E0), the set of emitted rampsconstituting a signal of duration N·T_(E0).

It consists thereafter in performing a double spectral analysis by FFTon N points:

a first spectral analysis on N points is carried out on the signalE*₀(t) obtained after sampling of E₀(t) determined on the basis of thesignal received r₀(t), 73, after emission of a an elementary ramp e₀(t),71, of duration T_(E0);

a second spectral analysis is carried out on a signal E*₁(t) consistingof N samples, each sample E₁(t_(n)) corresponding, for a given instantt_(n), to the value of the signal E₀(t) determined on the basis of thesignal r₀(t) received for the elementary frequency ramp, 71, emitted atthe nth recurrence. The second spectral analysis is thus carried out ona signal E*₁(t) determined on the basis of a signal r₁(t), of durationN·T_(E0), consisting of the N samples 81 retained.

According to the invention, the N instants t_(n) are chosen in such away that for the recurrence n, n varying from 0 (first recurrence) toN−1 (Nth recurrence), the instant t_(n) is expressed by:

$\begin{matrix}{t_{n} = {{n \cdot T_{E\; 0}} + {n \cdot \frac{T_{E\; 0}}{N}}}} & \lbrack 29\rbrack\end{matrix}$

Accordingly, the N points 81 constituting the samples of the signalr₁(t), each having as abscissa an instant t_(n) in a time-frequencyrepresentation, correspond to N points aligned along a straight line ofslope K₁ which is smaller than the slope K₀ characterizing theelementary ramps 71, K₁ being expressed by:

$\begin{matrix}{K_{1} = \frac{K_{0}}{N}} & \lbrack 30\rbrack\end{matrix}$

In this way an emission signal 73 of duration N·T_(E0) having the formof a frequency ramp e₁(t) of slope K₁ is synthesized in a virtualmanner.

Advantageously the corresponding reception signal, r₁(t), 75, is thendefined by N samples 81 of the signals r₀(t), 72, corresponding to thevalue of the signal received at each instant t_(n) subsequent to theemission of the frequency ramp 71 of slope K₀ of the n^(th) recurrence.

This second form of implementation thus makes it possible, by emitting asingle type of frequency ramps of slope K₀, to have, as in the case ofthe previous form of implementation, two signals E₀ and E₁, byimplementing the double spectral analysis processing of E*₀(t) andE*₁(t) implemented by the method according to the invention. However,the formation of the signal E₁(t), carried out in the course of step 32,appears different.

Thus, to form the signal E*₁(t), an aggregation is carried out ofsamples over N recurrences corresponding to the N elementary ramps 71emitted.

It should however be noted that the aggregation of the samples over Nrecurrences must be done with a delay compensation proportional to therank of the recurrence.

Indeed, if the signal e₀(t,n) of the signal corresponding to anelementary ramp 71 of rank n (n varying from 0 to N−1) is considered, itis noted that this elementary ramp is defined for tϵ[0+τ_(max); T_(E1)]by:e ₀(t,n)=e ^(i·2·π·K) ⁰ ^(·(t−n·T) ^(E0) ^(−τ) ^(max) ^()·t)  [31]

Accordingly, to perform the aggregation of the samples of the signalsE₀(t) over N recurrences, it is necessary to create a replica of theemitted wave e_(r)(t,n) and to add, at each recurrence, a phase equal to

$n \cdot \frac{2 \cdot \pi}{N}$so as to apply it to the reception LO (Local Oscillator) of the radarreceiver, in such a way as to be able to form a measurement signal whoseperiod is >T_(E0).

Thus, after phase shift of the LO, we obtain e_(r)(t,n) and r₀(t,n)which are given by the following relations:

$\begin{matrix}{{e_{r}\left( {t,n} \right)} = e^{{{i \cdot 2 \cdot \pi}\mspace{11mu}\ldots\mspace{11mu}{K_{0} \cdot {({t - {n \cdot T_{E\; 0}} - \tau_{{ma}\; x}})} \cdot t}} + {n \cdot \frac{2 \cdot \pi}{N}}}} & \lbrack 32\rbrack \\{{r_{0}\left( {t,n} \right)} = e^{{i \cdot 2 \cdot \pi}\mspace{11mu}\ldots\mspace{11mu}{K_{0} \cdot {({t - {n \cdot T_{E\; 0}} - \tau_{{ma}\; x} - \tau})} \cdot t}}} & \lbrack 33\rbrack\end{matrix}$

The signal E*₁(t) is thus defined, for t∈[0+τ_(max), T_(E1)], by thefollowing expression:

$\begin{matrix}{{E_{1}^{*}(t)} = {\frac{e_{r}\left( {t,n} \right)}{r_{0}\left( {t,n} \right)} = e^{i \cdot 2 \cdot {\Pi{({{K\;\tau\; t} + \frac{n}{N}})}}}}} & \lbrack 34\rbrack\end{matrix}$

It should be noted here, that in an advantageous manner the samples ofthe signals E*₀(t) aggregated over the N recurrences are tapped off atparticular instants specific for each of the recurrences. Thus, for thenth recurrence, we tap off the sample corresponding to the instant t_(n)defined by the relation:

$t_{n} = {n \cdot {{T_{E\; 0}\left( \frac{N + 1}{N} \right)}.}}$

It may readily be noted that, if the samples of the signals E*₀(t)aggregated over the N recurrences are tapped off at identical instantst_(n)=N·T_(E0) for each recurrence, the signal E*₁(t) is then defined,for t∈[0+τ_(max), T_(E1)], by the following expression:

$\begin{matrix}{{E_{1}^{*}(t)} = {\frac{e_{r}\left( {t_{n},n} \right)}{r_{0}\left( {t_{n},n} \right)} = e^{i \cdot 2 \cdot \Pi \cdot {n{({{K \cdot \;\tau \cdot \; T_{E\;{0 \cdot}}} + \frac{1}{N}})}}}}} & \lbrack 35\rbrack\end{matrix}$

Accordingly, in the case where the period

$T_{E\; 0} \cdot \frac{N + 1}{N}$is smaller than

$\frac{1}{K \cdot \tau},$we can write

$\begin{matrix}{{E_{1}^{*}(t)} = {\frac{e_{r}\left( {t_{n},n} \right)}{r_{0}\left( {t_{n},n} \right)} = e^{i \cdot 2 \cdot \Pi \cdot {n{({\gamma + \frac{1}{N}})}}}}} & \lbrack 36\rbrack\end{matrix}$with γ=K·τ·T_(E0).

E*₁(t) therefore appears to be a signal of frequency

$F = {\gamma + \frac{1}{N}}$

and we can write, for

$\frac{1}{K \cdot \tau} < {T_{E\; 0}\text{:}}$

$\begin{matrix}{F_{{ma}\; x} = {{\frac{1}{2 \cdot T_{E\; 0}}\mspace{14mu}{and}\mspace{14mu} F_{\min}} = \frac{1}{N \cdot T_{E\; 0}}}} & \lbrack 37\rbrack\end{matrix}$

On the other hand, if the samples of the signals E*₀(t) aggregated overthe N recurrences are tapped off as indicated above, for distinctinstants t_(n), we can write

$\begin{matrix}{{E_{1}^{*}(t)} = {\frac{e_{r}\left( {t,n} \right)}{r_{0}\left( {t,n} \right)} = e^{{i \cdot 2 \cdot \Pi}\;{n{({\gamma + \frac{1}{N}})}}}}} & \lbrack 38\rbrack\end{matrix}$with

$\gamma = {K \cdot \tau \cdot T_{E\; 0} \cdot \left( \frac{N + 1}{N} \right)}$

The signal E*₁(t) being defined on N points spaced apart by

$\frac{N + 1}{N}.$T_(E0), we note the existence of a scale factor equal to

$\frac{N}{N + 1}$on the quantization or frequency F of the signal which is in this casedefined, for

${\frac{1}{K \cdot \tau} < {T_{E\; 0} \cdot \left( \frac{N + 1}{N} \right)}},$by the relation:

$\begin{matrix}{F = {\left( {\frac{1}{\gamma} + \frac{1}{N}} \right) \cdot \frac{N}{N + 1}}} & \lbrack 39\rbrack\end{matrix}$F_(min) and F_(max) then being defined by:

$\begin{matrix}{F_{m\; i\; n} = {{\frac{1}{\left( {N + 1} \right) \cdot T_{E\; 0}}\mspace{14mu}{and}\mspace{14mu} F_{{ma}\; x}} = \frac{N}{2 \cdot \left( {N + 1} \right) \cdot T_{E\; 0}}}} & \lbrack 40\rbrack\end{matrix}$

It is thus noted that the samples collection principle implemented inthe context of the invention advantageously makes it possible toincrease the frequency resolution, without changing the parameters ofthe waveform that is used.

The invention claimed is:
 1. A method for determining in real time thedistance, d, from the ground of an aircraft by radar measurements, thesaid distance d being determined, for a span of distances extending upto a given distance d_(max), with a given constant resolution R_(d0);wherein it implements the following operations: the emission of at leasttwo successive frequency ramps and the reception of the signalsreflected by the ground subsequent to these emissions; the construction,on the basis of the reflected signals received of two signals E₀(t) andE₁(t) each corresponding to the reflected signal r₀(t) or r₁(t)originating from the successive emissions of two waveforms e₀(t) ande₁(t), after demodulation of the signals r₀(t) and r₁(t) by thecorresponding wave e₀(t) or e₁(t) and sampling of the demodulated signalat a given frequency F_(éch); the said waveforms e₀(t) and e₁(t) beingrepresented in a “time-frequency” space by two frequency rampsexhibiting respective slopes of variation K₀ and K₁, on two frequencybands B₀ and B₁ whose ratio B₁/B₀ is a given integer number, the band B₀being determined as a function of the distance resolution R_(d0) by therelation:B ₀ = ^(c)/2R _(d0), the slope K₁ being determined as a function of thedistance d_(max) by the relation:${K_{1} = {\frac{c}{2} \cdot \frac{F_{\overset{\prime}{e}{ch}}}{2{\alpha \cdot d_{1{ma}\; x}}}}};$the slopes K₀ and K₁ being respectively given by the relationsK ₀ = ^(B) ₀ /T _(E0) and K ₁ = ^(B) ₁ /T _(E1) where T_(E0) and T_(E1)represent the respective durations of emission of the waveforms e₀(t)and e₁(t); the application of an FFT, on N samples, to the signals E₀(t)and E₁(t) and determination of the spectral components E₀ and E₁corresponding to the said signals, E₀ corresponding to the component oflowest frequency of the spectrum of E₀(t); the determination, on thebasis of the spectral components E₀ and E₁, of the distances measured d₀and d₁ by means of the waveforms e₀(t) and e₁(t) correspondingrespectively to the spectral components E₀ and E₁, d₀ and d₁ being givenby the relations:$d_{0} = {{{\frac{c}{2} \cdot \frac{E_{0}}{\alpha\; K_{0}}}\mspace{14mu}{and}\mspace{14mu} d_{1}} = {\frac{c}{2} \cdot \frac{E_{1}}{\alpha\; K_{1}}}}$the determination, on the basis of d₀ and d₁, of the distance d to bemeasured, d being given by the relation:d=M·d _(0max) +d ₀ with$d_{0{ma}\; x} = {{\frac{c}{2} \cdot \frac{F_{0{ma}\; x}}{\alpha\; K_{0}}} = {{{\frac{c}{2} \cdot \frac{F_{\overset{\prime}{e}{ch}}}{2\alpha\; K_{0}}}\mspace{14mu}{and}\mspace{14mu} M} = {{{INT}\left( \frac{d_{1}}{d_{0{ma}\; x}} \right)} = {{{INT}\left( {2 \cdot E_{1} \cdot T_{\overset{\prime}{e}{ch}}} \right)}.}}}}$2. The method according to claim 1, wherein it comprises the followingsteps: a first step during which are determined the slopes K₀ and K₁,and frequency bands B₀ and B₁ characterizing the two signals e₀(t) ande₁(t) as well as the durations of emission T_(E0) and T_(E1) of thesetwo signals; this first step being carried out while taking into accountthe following parameters: maximum distance measured: d_(max), distanceresolution required: R_(d0), frequency of sampling of the signalsreceived by the radar: F_(éch), number N of points on which the spectraldecomposition of the signals must be performed; a second step ofemission during which: the radar emits at least two waves correspondinga chosen type of emission, at least one of these waves consisting of afrequency ramp of band B₀ and of slope K₀; the radar receives thereflected signals resulting from the reflection by the ground of theemitted waves; the signals E₀(t) and E₁(t) are formed on the basis ofthe reflected signals received; a third step during which are carriedout the spectral decomposition by FFT on N points of the signals E₀(t)and E₁(t) and the determination of the spectral components E₀ and E₁; afourth step during which is carried out the calculation of the distanced on the basis of E₀ and E₁.
 3. The method according to claim 2, whereinthe fourth step 34 comprises: a first sub-step of calculating thedistance d₁ defined by:$d_{1} = {\frac{c}{2} \cdot \frac{G_{1}}{\alpha\; K_{1}}}$ where G₁represents the integer part of the spectrum of E1(t) a second sub-stepof calculating the scale factor M defined by:${M = {{INT}\left( \frac{2E_{1}}{F_{\overset{\prime}{e}{ch}}} \right)}};$a third sub-step of calculating the distance d₀ defined by:$d_{0} = {\frac{c}{2} \cdot \frac{H_{0}}{\alpha\; K_{0}}}$ where H₀represents the integer part of the value of the first spectral line, E₀,of the spectrum of E0(t); a fourth sub-step of calculating the distanced, defined by: d=M·d_(0max)+d₀.
 4. The method according to claim 2,wherein the waveforms emitted by the radar in the course of the secondstep of the method consist of a first frequency ramp e₀(t) of band B₀and of slope K₀ followed by a second frequency ramp e₁(t) of band B₁ andof slope K₁.
 5. The method according to claim 4, wherein the signale₀(t) and the signal e₁(t) have distinct durations of respectiveemission T_(E0) and T_(E1) and occupy one and the same frequency band B,so that their respective slopes K₀ and K₁ are expressed by:$K_{0} = {{\frac{B}{T_{E\; 0}}\mspace{14mu}{and}\mspace{14mu} K_{1}} = {\frac{B}{T_{E\; 1}}.}}$6. The method according to claim 4, wherein the signals E₀(t) and E₁(t)are obtained after demodulation of the signals received r₀(t) and r₁(t)by the signals emitted e₀(t) and e₁(t), the signals E₀(t) and E₁(t)being thereafter sampled in the course of the third step at thefrequency F_(éch) so as to obtain the signals E*₀(t) and E*₁(t), the FFTspectral analysis of which is carried out.
 7. The method according toclaim 2, wherein the waveforms emitted by the radar in the course of thesecond step of the method consist of a recurrent string of N identicalfrequency ramps e₀(t−nT_(E0)), mutually shifted in time by a durationT_(E0) equal to the emission time of a ramp, of band B and of durationT_(E0).
 8. The method according to claim 7, wherein for each of the Nfrequency ramps emitted, the signal E₀(t) obtained by demodulation ofthe signal received by the signal emitted is sampled to obtain thecorresponding signal E*₀(t), and then a signal E*₁(t) is constructed byconsidering a sample of the signal E*₀(t) formed for each of the N rampsemitted, the signal E*₁(t) consisting of the N samples thus tapped off.9. The method according to claim 8, wherein for the nth frequency rampe₀(t) emitted the signal received r₀(t) is demodulated by applying aphase shift equal to $n \cdot \frac{2 \cdot \pi}{N}$ to the localoscillator of the radar receiver.
 10. The method according to claim 8,wherein for each of the N signals E*₀(t) formed, one taps off the samplecorresponding the instant t_(n) determined by the expression:${t_{n} = {{n \cdot T_{E\; 0}} + {n \cdot \frac{T_{E\; 0}}{N}}}},$ inwhich n represents the rank, in the string of frequency ramps emitted,of the frequency ramp n corresponding to the signal E*₀(t) considered.